在计算机上解决和玩扑克纸牌的注意事项
Notes on solving and playing peg solitaire on a computer
摘要：
我们考虑在计算机上玩的单人纸牌游戏。两种流行的棋盘形状是33孔的十字形棋盘和15孔的三角形棋盘-我们自始至终都用它们作为例子。基本游戏从一个完整的棋盘开始，缺少一个钉子，目标是在一个棋盘位置结束。首先，我们讨论在计算机上解决基本游戏的方法。然后，我们考虑快速区分目标仍然可以达到（“获胜”的董事会位置）的董事会位置与那些不能达到的位置的问题。这使计算机能够提醒玩家，如果正在考虑的跳跃导致死胡同。在15洞三角形棋盘上，通过存储437个棋盘位置的密钥集，可以识别所有获胜的棋盘位置（从任何一个空缺开始）。对于33孔十字形棋盘上的“中心局”，我们可以通过存储839，536个棋盘位置来识别所有获胜的棋盘位置。通过将一个成功的游戏看作是对获胜棋盘位置的有向图的遍历，我们应用一个简单的算法来计算遍历这个图的方法的数量，并计算出中心游戏的解的总数为40，861，647，040，079，968。我们的分析还可以确定我们可以多快到达“死板位置”，在那里一个钉完成不再是可能的。
英文摘要：
We consider the one-person game of peg solitaire played on a computer. Two popular board shapes are the 33-hole cross-shaped board, and the 15-hole triangle board---we use them as examples throughout. The basic game begins from a full board with one peg missing and the goal is to finish at a board position with one peg. First, we discuss ways to solve the basic game on a computer. Then we consider the problem of quickly distinguishing board positions where the goal can still be reached ("winning" board positions) from those where it cannot. This enables a computer to alert the player if a jump under consideration leads to a dead end. On the 15-hole triangle board, it is possible to identify all winning board positions (from any single vacancy start) by storing a key set of 437 board positions. For the "central game" on the 33-hole cross-shaped board, we can identify all winning board positions by storing 839,536 board positions. By viewing a successful game as a traversal of a directed graph of winning board positions, we apply a simple algorithm to count the number of ways to traverse this graph, and calculate that the total number of solutions to the central game is 40,861,647,040,079,968. Our analysis can also determine how quickly we can reach a "dead board position", where a one peg finish is no longer possible.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
